Tires for 3/4 4x4

I want to get new tires and rims for my 1999 2500 4x4 ext. cab silverado. I was wondering what the biggest tires are I can put on. I would like for them to stick out from the wells a little bit. I like that look better. Would I have to go smaller to get wider with out rubbing? Thanks Butch

275/70 will fit anything bigger will rub